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Equilibrium Positions and Eigenfunctions of Shape Invariant (`Discrete') Quantum Mechanics

S. Odake·R. Sasaki
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Abstract

Certain aspects of the integrability/solvability of the Calogero-Sutherland-Moser systems and the Ruijsenaars-Schneider-van Diejen systems with rational and trigonometric potentials are reviewed. The equilibrium positions of classical multi-particle systems and the eigenfunctions of single-particle quantum mechanics are described by the same orthogonal polynomials: the Hermite, Laguerre, Jacobi, continuous Hahn, Wilson and Askey-Wilson polynomials. The Hamiltonians of these single-particle quantum mechanical systems have two remarkable properties, factorization and shape invariance.

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S. Odake, R. Sasaki. 2005-05-09. Equilibrium Positions and Eigenfunctions of Shape Invariant (`Discrete') Quantum Mechanics. https://arxiv.org/abs/hep-th/0505070

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